Complete the statements to verify that f(x) = 10x and g(x) = log10x are inverses of each other. f(g(x)) = 10log10x Using the law of logarithms blogbn = , we have that f(g(x)) = . We also need to show that is also equal to x. g(f(x)) = log10(10x) Using the law of logarithms logbbn = , which means that g(f(x)) = x. Therefore, f and g are inverses of each other.
Answers
Complete the statements to verify that f(x) = 10x and g(x) = log10x are inverses of each other. f(g(x)) = 10log10x
The answer is given below in the image.
What are the two laws of logarithms?The laws apply to logarithms of any base but the identical base needs to be used at some point in a calculation. This regulation tells us a way to add logarithms collectively. Adding log A and log B results in the logarithm of the product of A and B, that is log AB. The same base, in this situation 10, is used throughout the calculation.
What is the fundamental law of logarithms?A logarithm of more than a few raised to a power is identical to the power expanded via the logarithm of the wide variety to the same base. that is, loga(mn) = nlogam.
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Related Questions
Determine whether the relation represents y as a function of x
2x+y^2=6
Answers
Answer:
rabi pati le crabby pati vi qui faste un fadi xx
1. Function s is y = 5x - 4
(a) What is the inverse of function s? Show steps to finding it.
(b) Graph the function & its inverse on the same grid. Show at least 3 points on each line.
(c) Is the inverse of function s a function? Explain your answer.
Answers
Answer:
duhuhduiwehiufhewufuewgewfguiwgf
Step-by-step explanation:
Which phrase is equivalent to “Franco must work a minimum of 32 hours”? The number of hours Franco works must be less than 32. The number of hours Franco works must be greater than 32. The number of hours Franco works must be less than or equal to 32. The number of hours Franco works must be greater than or equal to 32.
Answers
Answer:
The number of hours Franco works must be greater than or equal to 32.
Step-by-step explanation:
The number of hours Franco works is greater than or equal to 32. Then the correct option is D.
What is inequality?Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as well as is used to compare two statements.
The statement is given below.
“Franco must work a minimum of 32 hours”
Let x be the number of hours France works.
According to the statement, the inequality equation will be given as
x ≥ 32
The number of hours Franco works is greater than or equal to 32.
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Can you please help
Solve: x/2 = 7
Answers are:
x=5
X=7
X=9
X=14
Answers
Answer:
X = 14
14/2=7
Answer:
x=7
Step-by-step explanation:
you multiply a 2 to one already there and it eliminates the 2 entirely and then you get x=7
what is 2*2 please answer this question
Answers
Answer:
4
Step-by-step explanation:
Answer:
5-1
Step-by-step explanation:
Which of the following steps should be completed first when simplifying ?
Answers
Answer:C
Step-by-step explanation:
If a person drives his car in the speed 50 miles per hour, how far can he cover the distance in 2.5 hours ?
Answers
Answer:
Hey there!
50 miles = 1 hour
x miles = 2.5 hours
50/1= x/2.5
x=2.5x50
x=125
The car can go 125 miles.
Hope this helps :)
Answer:
125miles
Step-by-step explanation
distance=speed *time
d=50*2.5
d=125m
If f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?
12
14
36
38
Answers
Answer: 14
Step-by-step explanation:
Brian is planning to donate 13% of his income to charity. His weekly paycheck is $667.63. How much does Brian plan to donate?
Answers
Answer:
Brian is planning on donating $86.79.
Step-by-step explanation:
The first step is to write 13% in decimal form. We then multiply, .13 x 667.63=$86.79
Identify the domain of the function shown in the graph.
O A. -7 sys7
B. xso
C. y= 1.5
O O
D. xis all real numbers.
Answers
Answer. X is all real numbers
Step-by-step explanation:
Did it on apex
divide 5346 divided by 29
Answers
Answer:
184.3448276
Step-by-step explanation:
5346/29
184.3448276
Answer:
594
Step-by-step explanation:
Determine whether the following graph represents a function.
A.function
B. Not function
Answers
b i think...
lmk if it's wrong, if it is i'm sooooo sorry!!
:)
How would the underline look like
Answers
Answer:
the correct answer is C
Question 3
1 pts
Which number could be used as a counterexample to show that the conjecture
"All multiples of 3 are odd" is false?
12
027
O 33
O 15
Answers
The correct answer is A. 12
Explanation:
In mathematics, odd numbers are those numbers that cannot be divided into 2 without using a decimal number, for example, 13 ÷ 2 = 2.5 (decimal number). This does not occur with even numbers such as 26 because these can be divided into 2 and the result is an integer rather than a decimal (26 ÷ 2 =13).
On the other hand, a counterexample is a situation that shows an exception to the rule. In the rule "All multiples of 3 are odd", one counterexample is the number 12 because this is an even number (12 ÷2 = 6). Moreover, this number is a multiply of 3 as 3 can be multiplied by 4 to obtain 12, which shows multiplies of 3 can be even numbers.
Assume that the standard deviation of daily returns for Marcus, Inc. stock in a recent period is 1.5 percent. Furthermore, a 95 percent confidence interval is desired for the maximum loss. Daily returns are normally distributed, and the expected daily return is 0.05 percent. What is the lower boundary of the maximum expected loss
Answers
Answer:
= - 2.43%
Step-by-step explanation:
From the information given:
Since the variable (daily returns) is normally distributed, Then, using empirical rule at 95% confidence interval level, we have:
[tex]( \mu - 1.96 \sigma \ , \ \mu + 1.96 \sigma)[/tex]
where;
The expected mean daily return [tex]\mu = 0.05 \%[/tex]
The standard deviation [tex]\sigma = 1.5\%[/tex]
Given that the 95% confidence interval is expected to be a maximum loss, then the probability is left-tailed which is 1.65[tex]\sigma[/tex] away from the average.
Thus the distribution of the lower boundary can be computed as:
= [tex](0.05 - 1.65 \times 1.5)\%[/tex]
= [tex](0.05 - 2.475)\%[/tex]
= [tex]( - 2.425)\%[/tex]
= - 2.43%
Which two expressions are equivalent?
A. 5x - 5 and 5(x - 5)
B. 5(x - 5) and 5x - 25
C. 5x - 1 and 5(x - 5)
D. 5x(x - 1) and 5x - 5
Answers
Answer:
B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
If the temperature is -4 and rises by 12 , what is the new temperature ?
Answers
Answer:
-4 +12 = 8
the new temperature is 8 degree
Step-by-step explanation:
The sum of two numbers is 50. The first number is 18 less than the 2nd number. What are the
2 numbers?
Answers
Answer:
2y + 2 + y = 50 (combine like terms)
3y + 2 = 50
3y = 50 - 2
3y = 48
y = 16
Substitute 16 for y in either equation 1 or 2 and solve for x (I chose equation 1):
x + 16 = 50
x = 50 - 16
x = 34
Step-by-step explanation:
Joe has saved $50. He wants to
buy 3 graphic novels that cost $13 each.
Can Joe afford the graphic novels?
Answers
Answer:
Yes, Joe can afford the graphic novels.
Explanation:
Joe has $50Each graphic novel costs $13Joe wants 3 graphic novels[ Multiply ]
13 · 3 = 39
Joe will be spending at total of $39 if he buys 3 graphic novels. He will have a total of $11 left over. Joe can afford the graphic novels.
Which table corresponds to the graph of the function below?
Answers
Answer:
I belive its the second 1
Step-by-step explanation:
kakalkjslkajslkjslkjalk
Answer: A is the answer
Step-by-step explanation:
I need help I’ll give you points it’s urgent
Answers
Answer:
Step-by-step explanation:
Area: 28.26
Circumference: 12.56
What is the solution of the inequality x3 + 3x2 > 7x + 6?
Answers
Answer:
Inequality form : - 5 + squareroot13 / 2 < x < - 5- squareroot13 / 2 or x > 2
Step-by-step explanation: Solve the inequality by finding the roots and creating test intervals.
I hope this helps you out! :)
The solution to the inequality is [tex]\rm \left (\dfrac{-5+\sqrt{13} }{2} < x < \dfrac{-5-\sqrt{13} }{2} \right ) \ or \ x > 2[/tex].
The Interval Notation is [tex]\rm \left (\dfrac{-5+\sqrt{13} }{2} , \dfrac{-5-\sqrt{13} }{2} \right ) \cup (2, \infty)[/tex].
What is inequality?In Mathematics, the relationship between two values that are not equal is defined by inequalities.
The given inequality is;
[tex]\rm x^3 + 3x^2 > 7x + 6[/tex]
The solution to the inequality is determined in the following steps given below.
[tex]\rm x^3 + 3x^2 > 7x + 6\\\\\rm x^3 + 3x^2-7x-6 > 7x + 6-7x-6\\\\ x^3 + 3x^2-7x-6 > 0\\\rm \\ x(x^2+5x+3)-2(x^2+5x+3) > 0\\\\ \rm x^3+5x^2+3x-2x^2-10x-6 > 0\\\\ x(x^2+5x+3)-2(x^2+5x+3) > 0\\\\\rm (x-2)(x^2+5x+3) > 0[/tex]
Now finding the roots of the inequality;
[tex]\rm (x-2)(x^2+5x+3) > 0 \\\\(x-2) \left (\dfrac{-5\pm\sqrt{25-12} }{2} \right )\\\\(x-2)\left (\dfrac{-5+\sqrt{13} }{2} \right )\left (\dfrac{-5-\sqrt{13} }{2} \right )[/tex]
Hence, the solution to the inequality is [tex]\rm \left (\dfrac{-5+\sqrt{13} }{2} < x < \dfrac{-5-\sqrt{13} }{2} \right ) \ or \ x > 2[/tex].
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Andrew was making a science project for school. He worked for 6.6 hours the first week, 2.75 hours the second week, and 4.4 hours the third week.
Andrew used the following mental math strategy to find the total number of hours he worked on his project.
Answers
Answer:
Step-by-step explanation:
its wierd but 2.22
-6n-32m+5n
Need help please
Answers
Answer:
Add
−
6 n and 5n.− 32m − n
Step-by-step explanation:
In segment AC, the midpoint is B. If segments AC = 8 AB = 3x-1 find x.
Answers
Answer:
If B is the midpoint, it means
AC=2AB
8= 2(3x-1)
8= 6x-2
8+2= 6x
10= 6x
x= 10/6
x= 1.67
Hope it helps :-)
What number is the opposite of 3.5
Answers
Answer:
-2/7
Step-by-step explanation: Thats the reciprocal so...
Find the volume of a cylinder with height 25cm and radius 5cm
Answers
Answer:
1963.5
-------------
Answer:
1,932 cm approxmately.
Step-by-step explanation:
Your formula is V= π5²h
V= 3.14 x 5² x 25
V= ≈1932 cm
MATCH THE EXPRESSIONS WITH THE VARIABLES IN IT! HELP I APPRECIATE IT
Answers
x:
[tex]3x^{2} +x+9[/tex]
y:
[tex]4y+7[/tex]
[tex]6y^{2} +y+3[/tex]
x and y:
[tex]2x-3y^{3} -4[/tex]
[tex]5x+3y+6[/tex]
what is 3/4 - (-4/5)
Answers
Answer: 1,55
Step-by-step explanation:
3/4 - (- 4/5) = 3/4 + 4/5 = (3x5)/20 + (4x4)/20 = 15/20 + 16/20 = 31/20 = 1,55
3/4 - (- 4/5) = 3/4 + 4/5 = 0,75 + 0.8 = 1,55
make doubles. add 5+6
Answers
Answer:11
Step-by-step explanation: